Video Lectures

Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random variable...

We will discuss interactive coding in the setting where there are n parties attempting to compute a joint function of their inputs using error-prone pairwise communication channels. We will present a general protocol that allows one to achieve only...

I will present some recent applications of symplectic geometry to the restricted three body problem. More specifically, I will discuss how Gromov's original study of pseudoholomorphic curves in the complex projective plane has led to the...

We will outline the proof that gives a positive solution of to Weaver's conjecture \(KS_2\). That is, we will show that any isotropic collection of vectors whose outer products sum to twice the identity can be partitioned into two parts such that...

I will discuss the proof by Yang Kang and myself of diffusion for the Markov Anderson model, in which the potential is allowed to fluctuate in time as a Markov process. However, I want to highlight the method of the proof more than the result itself...

One of the major open problems in complexity theory is proving super-polynomial lower bounds for circuits with logarithmic depth (i.e.,\(P \not\subseteq NC_1\) ). This problem is interesting both because it is tightly related to understanding the...

The study of random Cayley graphs of finite groups is related to the investigation of Expanders and to problems in Combinatorial Number Theory and in Information Theory. I will discuss this topic, describing the motivation and focusing on the...

To any bounded family of \(\mathbb F_\ell\)-linear representations of the etale fundamental of a curve \(X\) one can associate families of abstract modular curves which, in this setting, generalize the `usual' modular curves with level \(\ell\)...